Consider the set of all possible five-card poker hands dealt fairly from a…
2018
Consider the set of all possible five-card poker hands dealt fairly from a standard deck of fifty-two cards. How many atomic events are there in the joint probability distribution ?
- A.
2, 598, 960
- B.
3, 468, 960
- C.
3, 958, 590
- D.
2, 645, 590
Attempted by 89 students.
Show answer & explanation
Correct answer: A
Key idea: the number of distinct five-card hands equals the number of ways to choose 5 cards from 52 when order does not matter.
Use the combination formula: C(52,5) = 52! / (5!·47!) = (52×51×50×49×48) / (5×4×3×2×1).
Simplify by canceling factors: 50/5 = 10, 48/4 = 12, 51/3 = 17, 52/2 = 26, giving 26×17×10×49×12.
Compute stepwise: 26×17 = 442; 442×10 = 4,420; 4,420×49 = 216,580; 216,580×12 = 2,598,960.
Therefore the number of atomic events in the joint probability distribution (the number of distinct five-card hands) is 2,598,960.
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